Stochastic simulation model for the 3D morphology of composite materials in Li–ion batteries

Abstract Battery technology plays an important role in energy storage. In particular, lithium–ion (Li–ion) batteries are of great interest, because of their high capacity, long cycle life, and high energy and power density. However, for further improvements of Li–ion batteries, a deeper understanding of physical processes occurring within this type of battery, including transport, is needed. To provide a detailed description of these phenomena, a 3D representation is required for the morphology of composite materials used in Li–ion batteries. In this paper, we develop a stochastic simulation model in 3D, which is based on random marked point processes, to reconstruct real and generate virtual morphologies. For this purpose, a statistical technique to fit the model to 3D image data gained by X-ray tomography is developed. Finally, we validate the model by comparing real and simulated data using image characteristics which are especially relevant with respect to transport properties.

[1]  Dieter Jungnickel,et al.  Graphs, Networks, and Algorithms , 1980 .

[2]  Ann Marie Sastry,et al.  Two-Dimensional vs. Three-Dimensional Clustering and Percolation in Fields of Overlapping Ellipsoids , 2004 .

[3]  B. N. Chatterji,et al.  Anisotropic Diffusion in Image Processing: Methods based on Physics, Statistics and Geometric Curve Evolution , 2002 .

[4]  A. Sastry,et al.  Compression of Packed Particulate Systems: Simulations and Experiments in Graphitic Li-ion Anodes , 2006 .

[5]  R. García-Pelayo.  Distribution of distance in the spheroid , 2005 .

[6]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[7]  Grégoire Malandain,et al.  Blockwise processing applied to brain microvascular network study , 2006, IEEE Transactions on Medical Imaging.

[8]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[9]  Stephen J. Harris,et al.  Measurement of three-dimensional microstructure in a LiCoO2 positive electrode , 2011 .

[10]  Yang-Tse Cheng,et al.  Mesopores inside electrode particles can change the Li-ion transport mechanism and diffusion-induced stress , 2010 .

[11]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[12]  I. Manke,et al.  Local Structural Characteristics of Pore Space in GDLs of PEM Fuel Cells Based on Geometric 3D Graphs , 2009 .

[13]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[14]  W. Kendall,et al.  New Perspectives in Stochastic Geometry , 2010 .

[15]  M. Verbrugge,et al.  Electrochemical analysis of lithiated graphite anodes , 2003 .

[16]  Daryl J. Daley,et al.  An Introduction to the Theory of Point Processes , 2013 .

[17]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[18]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .

[19]  D. Stoyan,et al.  Statistical Analysis and Modelling of Spatial Point Patterns , 2008 .

[20]  V. Schmidt,et al.  A MULTISCALE APPROACH TO THE REPRESENTATION OF 3D IMAGES, WITH APPLICATION TO POLYMER SOLAR CELLS , 2011 .

[21]  Lorenz Holzer,et al.  Contradicting Geometrical Concepts in Pore Size Analysis Attained with Electron Microscopy and Mercury Intrusion , 2008 .

[22]  Matthew D. Jackson,et al.  Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. , 2002 .

[23]  Volker Schmidt,et al.  Random geometric graphs for modelling the pore space of fibre-based materials , 2011 .

[24]  A. Gelfand,et al.  Handbook of spatial statistics , 2010 .

[25]  V. Schmidt,et al.  Spatial modeling of the 3D morphology of hybrid polymer-ZnO solar cells, based on electron tomography data , 2011, 1111.5145.

[26]  D. Stoyan,et al.  Stochastic Geometry and Its Applications , 1989 .

[27]  Volker Schmidt,et al.  The effect of three-dimensional morphology on the efficiency of hybrid polymer solar cells. , 2009, Nature materials.

[28]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[29]  Jun-ichiro Toriwaki,et al.  New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications , 1994, Pattern Recognit..

[30]  Nigel P. Brandon,et al.  Characterization of the 3-dimensional microstructure of a graphite negative electrode from a Li-ion battery , 2010 .